Antiferromagnetic Vortex Core in ${\mathrm{T}\mathrm{l}}_2{\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_{6+\delta }$ Studied by Nuclear Magnetic Resonance

Spatially resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally doped ${\mathrm{T}\mathrm{l}}_2{\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_{6+\delta }$ ($T_c=85\mathrm{K}$). The NMR relaxation rate $T_1^{-1}$ at the ${}^{205}\mathrm{T}\mathrm{l}$ site provides direct evidence that the antiferromagnetic (AF) spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers at $T_N=20\mathrm{K}$. Above $T_N$ the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature ($T^{*}\simeq 120\mathrm{K}$), indicating that the pseudogap disappears within cores.

Figure 1

Main panel: ${}^{205}\mathrm{T}\mathrm{l}\mathrm{\text{−}}\mathrm{N}\mathrm{M}\mathrm{R}$ spectrum (solid line) at 5 K. The intensity is plotted in a linear scale. The thin solid lines depict the histogram at particular local fields obtained from Eq. (1). In the calculation we used ${\xi }_{ab}=18\AA$ and ${\lambda }_{ab}=1700\AA$. The red dotted line represents the simulation spectrum convoluted with Lorentzian broadening function. The red filled circles show the frequency dependence of $T_1^{-1}$ at the Tl site. For details, see the text. Lower inset: ${}^{205}\mathrm{T}\mathrm{l}\mathrm{\text{−}}\mathrm{N}\mathrm{M}\mathrm{R}$ spectrum (solid line) and the simulation spectrum (red dotted line) at 20 K. In the calculation we used ${\xi }_{ab}=18.5\AA$ and ${\lambda }_{ab}=2000\AA$. Upper inset: the image of the field distribution in the vortex square lattice; center of vortex core (A), saddle point (B), and center of vortex lattice (C).

Figure 2

The linewidths of the ${}^{205}\mathrm{T}\mathrm{l}\mathrm{\text{−}}\mathrm{N}\mathrm{M}\mathrm{R}$ spectrum plotted as a function of $T$. $\Delta f$ (filled circles) indicates the linewidth determined by the frequency at which the intensity becomes 1% of the peak. The dashed line represents the linewidth calculated from the simulation spectrum without taking into account the core magnetism. Open circles represent $\delta f$ which is defined as the linewidth at the half intensity. The inset shows the spectrum at 5 K and the definition of $\Delta f$ and $\delta f$.

Figure 3

Recovery curves of nuclear magnetization of ${}^{205}\mathrm{T}\mathrm{l}$ as a function of time, $\tau$. The filled and open circles represent the data at the saddle points and at vortex cores, respectively. The inset shows the recovery curves at cores as a function of $\sqrt{\tau }$ at several temperatures.

Figure 4

(a) $T$ dependence of $({}^{205}T_{1}T{)}^{-1}$. (b) $T$ dependence of ${}^{205}T_1^{-1}$ at low temperatures (main panel) and at high temperatures (inset). The filled and open circles represent the data at vortex cores and at saddle points, respectively. $T^{*}\simeq 120\mathrm{K}$ is the pseudogap temperature. The dotted line represents the Curie-Weiss law which is determined above $T^{*}$. In (b), $T_N$ is the temperature at which ${}^{205}T_1^{-1}$ at the core exhibits a sharp peak.